The values of x in the triangles and the angles in the rhombus are illustrations of tangent ratios
- The values of x in the triangles are 21.4 units, 58 degrees and 66 degrees
- The angles in the rhombus are 44 and 46 degrees, respectively
<h3>How to determine the values of x?</h3>
<u>Triangle 1</u>
The value of x is calculated using the following tangent ratio
tan(25) = 10/x
Make x the subject
x = 10/tan(25)
Evaluate
x = 21.4
<u>Triangle 2</u>
The value of x is calculated using the following tangent ratio
tan(x) = 8/5
Evaluate the quotient
tan(x) = 1.6
Take the arc tan of both sides
x = arctan(1.6)
Evaluate
x = 58
<u>Triangle 3</u>
The value of x is calculated using the following tangent ratio
tan(x) = 0.34/0.15
Evaluate the quotient
tan(x) = 2.27
Take the arc tan of both sides
x = arctan(2.27)
Evaluate
x = 66
<h3>How to calculate the angles of the rhombus?</h3>
The lengths of the diagonals are:
L1 = 2 in
L2 = 5 in
Represent the angles with x and y.
The measures of the angles are calculated using the following tangent ratios
tan(0.5x) = 2/5 and y = 90 - x
Evaluate the quotient
tan(0.5x) = 0.4
Take the arc tan of both sides
0.5x = arctan(0.4)
Evaluate
0.5x = 22
Divide by 0.5
x = 44
Recall that:
y = 90 - x
This gives
y = 90 - 44
Evaluate
y = 46
Hence, the angles in the rhombus are 44 and 46 degrees, respectively
Read more about tangent ratio at:
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Answer:
<em>Martin saved $75 on the television because of the sale</em>
Step-by-step explanation:
<u>Equations</u>
Let's call x=the original price of the television (before discount).
The television had been on sale for 25% off, this means the discount was:
25% of x =
= 0.25x
The sale price was the original price minus the discount:
x - 0.25x = 0.75x
This is what Martin paid, thus:
0.75x = 225
Dividing by 0.75:
x = 225 / 0.75
x = $300
The original price of the television was $300, and the discount was:
0.25*$300 = $75
Martin saved $75 on the television because of the sale
She has to walk 60 minutes more to reach her goal.
Given: Flo sets a goal of walking 12,000 total steps per day. Flo's normal routine involves walking 6,000 steps per day.
To find: To Determine how many extra minutes should she walk per day beyond her normal routine?
Formula: Number of extra minutes = she walks per day beyond her normal routine / number of steps per minute
flo's normal routine involves walking steps per day= 6,000
If flo walks 100 steps per minute:
she walks per day beyond her normal routine = 
= 
Extra minutes = 
= 60 minutes
Therefore, she has to walk 60 minutes more to reach her goal.
Learn more about time and distance here brainly.com/question/24283318
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